code: def replace_variables(constraints, variables=None, markers="$"):
      """replace variables in constraints string with a marker.
      Returns a modified constraints string.
  
      Args:
          constraints (str): a string of symbolic constraints, with one constraint
              equation per line. Constraints can be equality and/or inequality
              constraints. Standard python syntax should be followed (the ``math``
              and ``numpy`` modules are already imported).
          variables (list[str], default=None): list of variable name strings.
              The variable names will be replaced in the order that they are
              provided. If the default marker ``"$i"`` is used, the first variable
              will be replaced with ``"$0"``, the second with ``"$1"``, and so on.
          markers (str, default='$'): desired variable name. A list of variable
              name strings is also accepted for when desired variable names
              don't have the same base.
  
      Examples:
          >>> variables = ['spam', 'eggs']
          >>> constraints = '''spam + eggs - 42'''
          >>> print(replace_variables(constraints, variables, 'x'))
          'x0 + x1 - 42'
  
          >>> variables = ['x1','x2','x3']
          >>> constraints = "min(x1*x2) - sin(x3)"
          >>> print(replace_variables(constraints, variables, ['x','y','z']))
          'min(x*y) - sin(z)'"""
      if variables is None:
          variables = []
      elif isinstance(variables, str):
          variables = list((variables,))
  
      # substitite one list of strings for another
      if list_or_tuple_or_ndarray(markers):
          equations = replace_variables(constraints, variables, "_")
          vars = get_variables(equations, "_")
          indices = [int(v.strip("_")) for v in vars]
          for i in range(len(vars)):
              equations = equations.replace(
                  vars[i], markers[indices[i]]
              )
          return equations
  
      # Sort by decreasing length of variable name, so that if one variable name
      # is a substring of another, that won't be a problem.
      variablescopy = variables[:]
      variablescopy.sort(key=lambda x: -len(x))
  
      # Figure out which index goes with which variable.
      indices = []
      for item in variablescopy:
          indices.append(variables.index(item))
  
      # Default is markers='$', as '$' is not a special symbol in Python,
      # and it is unlikely a user will choose it for a variable name.
      if markers in variables:
          marker = "_$$$$$$$$$$"  # even less likely...
      else:
          marker = markers
  
      '''Bug demonstrated here:
      >>> equation = """x3 = max(y,x) + x"""
      >>> vars = ['x','y','z','x3']
      >>> print(replace_variables(equation,vars))
      $4 = ma$1($2,$1) + $1
      '''  # FIXME: don't parse if __name__ in builtins, globals, or locals?
      for i in indices:  # FIXME: or better, use 're' pattern matching
          constraints = constraints.replace(
              variables[i], marker + str(i)
          )
      return constraints.replace(marker, markers)
  
imports: from numpy import ndarray, asarray, any
  from mystic._symbolic import solve
  from mystic.tools import list_or_tuple_or_ndarray, flatten
label_desc: Use image node_id 19 for calling a global function with example usage: replace_variables(constraints, variables, markers) and returns: constraints, equations